Stochastic quantum models for the dynamics of power grids

While electric power grids play a key role in the decarbonization of society, it remains unclear how recent trends, such as the strong integration of renewable energies, can affect their stability. Power oscillation modes, which are key to the stability of the grid, are traditionally studied numerically with the conventional viewpoint of two regimes of extended (inter-area) or localized (intra-area) modes. In this article we introduce an analogy based on stochastic quantum models and demonstrate its applicability to power systems. We show from simple models that at low frequency the mean free path induced by disorder is inversely cubic in the frequency. This stems from the Courant-Fisher-Weyl theorem [Teschl, Mathematical methods in quantum mechanics (American Mathematical Soc., 2014), Vol. 157], a characterization of the eigenvectors of the Laplacian of the network, which provides an intuitive understanding of how eigenvectors organize themselves into nodal domains resistant to disorder at low frequency. As a consequence, a power oscillation, induced by some local disruption of the grid, can propagate in a ballistic, diffusive, or localized regime. In contrast with the conventional viewpoint, the existence of these three regimes is confirmed in a realistic model of the European power grid.